The present invention relates to characterization of sample systems, and more particularly is a method of evaluating anisotropic sample system refractive indices, and orientations thereof, with respect to an alignment surface of said sample system, in multiple dimensions. The preferred method involves a sequence of steps which allows overcoming mathematical model parameter correlation during mathematical regression parameter evaluation, even though individually, steps of the present invention method wherein anisotropic refractive indices, or differences therebetween are evaluated, require that only a relatively simple one dimensional data set be acquired.
While many of the steps of the present invention can be practiced utilizing spectrophotometer systems, said present invention methodology is preferably practiced utilizing an ellipsometer/polarimeter system. The primary difference between ellipsometry/polarimetry and spectrophotometry is that the former evaluates changes in angle between orthogonal components of a polarized electromagnetic beam of radiation in addition to magnitudes, or more precisely a ratio of magnitudes thereof, as a result of interaction with a sample system. In that light it is further noted that ellipsometry is a well known means by which to monitor optical and physical properties of sample systems, (eg. an anisotropic substrate which possibly comprises thin films on a surface thereof). In brief, ellipsometry provides that a polarized beam of electromagnetic radiation of one or more wavelengths is caused to impinge upon a sample system along one or more angles of incidence and interact, (eg. reflect from or transmit through), therewith. Beams of electromagnetic radiation can be considered as comprised of two orthogonal components, (ie. xe2x80x9cPxe2x80x9d and xe2x80x9cSxe2x80x9d), where xe2x80x9cPxe2x80x9d identifies a plane which contains both an incident beam of electromagnetic radiation, and a normal to an investigated alignment surface of a sample system being investigated, and where xe2x80x9cSxe2x80x9d identifies a plane perpendicular to the xe2x80x9cPxe2x80x9d plane and parallel to said alignment surface of said sample system. A change in polarization state in a polarized beam of electromagnetic radiation caused by said interaction with a sample system, is representative of properties of said sample system. (Note that Polarization State basically refers to a magnitude of a ratio of orthogonal component magnitudes in a polarized beam of electromagnetic radiation, and a phase angle therebetween, although absolute values for orthogonal components and xe2x80x9chandednessxe2x80x9d, and even percent of polarization are further full polarization state determining factors). Generally two well known angles, (PSI and DELTA), which characterize a sample system at a given Wavelength and Angle-of-Incidence, are determined by analysis of data which represents change in polarization state. PSI is a ratio of the xe2x80x9cPxe2x80x9d and xe2x80x9cSxe2x80x9d component magnitudes, and DELTA is the phase angle therebetween. Again, spectrophotometer systems do not provide data regarding DELTA related phase angle, and often provide absolute rather than PSI ("psgr") type ratio intensity values. For instance, utilizing a transmission Jones matrix:       [                            Epo                                      Eso                      ]    ⁢                                          =                                                =                              ⁡              [                                            Tpp                                      Tsp                                                          Tps                                      Tss                                      ]              ⁢          xe2x80x83        [                            Epi                                      Esi                      ]  
to represent mathematically how a sample system affects a polarized electromagnetic beam, with Epi and Esi orthogonal components, and which is caused to interact therewith, it is to be appreciated that an ellipsometer/polarimeter system might return an on-diagonal ratio:                     (                  Tpp          /          Tss                )            =              Tan        ⁢                  xe2x80x83                ⁢                  (                      ψ                          pp              ss                                )                ⁢                  xe2x80x83                ⁢                  (                      ⅇ                          ⅈ              ⁢                              xe2x80x83                            ⁢                              Δ                                  pp                  ss                                                              )                      ;              and off-diagonal ratios:        ⁢          xe2x80x83                          (                  Tsp          /          Tss                )            =              Tan        ⁢                  xe2x80x83                ⁢                  (                      ψ                          sp              ss                                )                ⁢                  xe2x80x83                ⁢                  (                      ⅇ                          ⅈ              ⁢                              xe2x80x83                            ⁢                              Δ                                  sp                  ss                                                              )                      ;                      (                  Tps          /          Tss                )            =              Tan        ⁢                  xe2x80x83                ⁢                  (                      ψ                          ps              ss                                )                ⁢                  xe2x80x83                ⁢                  (                      ⅇ                          ⅈ              ⁢                              xe2x80x83                            ⁢                              Δ                                  ps                  ss                                                              )                      ;                      (                  Tsp          /          Tpp                )            =              Tan        ⁢                  xe2x80x83                ⁢                  (                      ψ                          sp              pp                                )                ⁢                  xe2x80x83                ⁢                  (                      ⅇ                          ⅈ              ⁢                              xe2x80x83                            ⁢                              Δ                                  sp                  pp                                                              )                      ;                      (                  Tps          /          Tpp                )            =              Tan        ⁢                  xe2x80x83                ⁢                  (                      ψ                          ps              pp                                )                ⁢                  xe2x80x83                ⁢                  (                      ⅇ                          ⅈ              ⁢                              xe2x80x83                            ⁢                              Δ                                  ps                  pp                                                              )                      ;  
as a function of a selection from the group consisting of:
angle-of-incidence;
wavelength; and
sample system rotation about a normal to said alignment surface.
A spectrophotometer system, however, might return Tpp, Tss, Tsp and/or Tps as a function of angle-of-incidence; wavelength; and/or sample system rotation about a normal to said alignment surface. It is to be understood that a reflection Jones Matrix       [                            Epo                                      Eso                      ]    ⁢                                          =                                                =                              ⁡              [                                            Rpp                                      Rsp                                                          Rps                                      Rss                                      ]              ⁢          xe2x80x83        [                            Epi                                      Esi                      ]  
could have also been utilized for said demonstration, and that generally the present invention method can be practiced utilizing data obtained with ellipsometer, polarimeter or spectrophotometer systems configured in transmission or reflection modes, and/or combinations thereof in any steps thereof, wherein functionality is preserved.
Continuing, Ellipsometer Systems generally include a source of a beam of electromagnetic radiation, a Polarizer, which serves to impose a linear state of polarization on a beam of electromagnetic radiation, a Stage for supporting a sample system, and an Analyzer which serves to select a polarization state in a beam of electromagnetic radiation after it has interacted with a sample system, and passed to a Detector System for analysis therein. As well, one or more Compensator(s) can be present and serve to affect a phase angle between orthogonal components of a polarized beam of electromagnetic radiation. This is especially important where it is necessary to determine the xe2x80x9cHandednessxe2x80x9d of a polarized beam of electromagnetic radiation.
A number of types of ellipsometer systems exist, such as those which include rotating elements and those which include modulation elements. Those including rotating elements include Rotating Polarizer (RP), Rotating Analyzer (RA), Rotating Compensator (RC) and Modulation element (ME). It is noted that Rotating Compensator Ellipsometer Systems do not demonstrate xe2x80x9cDead-Spotsxe2x80x9d where obtaining data is difficult. They can read PSI ("psgr") and DELTA (xcex94) of a sample system over a full Range of Degrees with the only limitation being that if PSI becomes essentially zero (0.0), one can not then determine DELTA as there is not a sufficient PSI ("psgr") Polar Vector Length to form the angle between the PSI ("psgr") Vector and an xe2x80x9cXxe2x80x9d axis. In comparison, Rotating Analyzer and Rotating Polarizer Ellipsometers have xe2x80x9cDead Spotsxe2x80x9d at DELTA""s (xcex94""s ) near 0.0 or 180 Degrees and Modulation Element Ellipsometers also have xe2x80x9cDead Spotsxe2x80x9d at PSI ("psgr") near 45 Degrees. The present invention method can be practiced with essentially any ellipsometer system.
A Search of Patents relevant to the present invention has identified very little of specific relevance. One Patent, to Dill, U.S. Pat. No. 4,053,232 describes a Rotating-Compensator Ellipsometer System, which operates utilizes monochromatic light. Two Patents which identify systems which utilize Polychromatic light in investigation of sample systems are described in U.S. Pat. Nos. 5,596,406 and 4,668,086, to Rosencwaig et al. and Redner, respectively, were also identified. Also identified is a Patent to Woollam et al, U.S. Pat. No. 5,373,359 as it describes a Rotating Analyzer Ellipsometer System which utilizes white light. Patents continued from the 359 Woollam et al. Patent are, U.S. Pat. No. 5,504,582 to Johs et al. and U.S. Pat. No. 5,521,706 to Green et al. Said 582 Johs et al. and 706 Green et al. Patents describe use of polychromatic light in a Rotating Analyzer Ellipsometer System. A Patent to Bernoux et al., U.S. Pat. No. 5,329,357 is identified as it describes the use of optical fibers as input and output means in an ellipsometer system. A Patent to Chen et al., U.S. Pat. No. 5,581,350 is identified as it describes the application of regression in calibration of ellipsometer systems.
A particularly interesting Patent to Herzinger, U.S. Pat. No. 5,835,222, is identified, and incorporated hereinto by reference, as it describes an ellipsometric based method for identifying the orientation of an optical axis in a material system with respect to an alignment surface thereof. One recitation of the method of the 222 Patent method of qualifying a material system as having an optical axis oriented in a desired locus with respect to an alignment surface thereof, comprises, in a functional order, the steps of:
a. by ellipsometric techniques determining the magnitudes of at least one member of the group consisting of:
real; imaginary; and a combination of real and imaginary components;
for at least one ratio of components of a material system representing transmission Jones matrix as a function of at least one member of the group consisting of:
wavelength; and
xe2x80x9cPxe2x80x9d plane angle-of-incidence of an investigating polarized beam of electromagnetic radiation to an alignment surface of said material system; and
optical axis radial direction rotation angle;
said at least one ratio of material system representing transmission Jones matrix components being selected from the group consisting of:
on-diagonal ratio:
(Tpp/Tss);
and off-diagonal ratios:
(Tsp/Tss);
(Tps/Tss);
(Tsp/Tpp);
(Tps/Tpp);
where Tpp, Tss, Tps and Tsp are the components of a two dimensional material system representing transmission Jones matrix:       [                            Epo                                      Eso                      ]    ⁢                                          =                                                =                              ⁡              [                                            Tpp                                      Tsp                                                          Tps                                      Tss                                      ]              ⁢          xe2x80x83        [                            Epi                                      Esi                      ]  
which material system representing transmission Jones matrix describes the change in polarization state between said incident and transmitted portions of said beam of electromagnetic radiation;
b. providing a mathematical model of said material system comprising at least one deviation angle calibration parameter which represents a non-coincidence of said optical axis with a desired locus with respect to said alignment surface, said mathematical model serving to relate indices of refraction, thickness and optical axis direction over a range of at least one member of the group consisting of:
wavelength; and
xe2x80x9cPxe2x80x9d plane angle-of-incidence of an investigating polarized beam of electromagnetic radiation to an alignment surface of said material system; and
optical axis radial direction rotation angle;
c. performing a regression procedure of said mathematical model onto said magnitude of at least one member of the group consisting of:
real;
imaginary; and
a combination of real and imaginary components;
of at least one step a. selected ratio of material system representing transmission Jones matrix components as a function of at least one member of the group consisting of:
wavelength;
xe2x80x9cPxe2x80x9d plane angle-of-incidence of an investigating polarized beam of electromagnetic radiation to an alignment surface of said material system; and
optical axis radial direction rotation angle;
such that said at least one deviation angle calibration parameter is evaluated.
Material systems are accepted if the deviation angle is small enough to fall within selected guidelines.
Said method of qualifying a material system as having an optical axis oriented in a desired locus with respect to an alignment surface thereof can further comprising the step of;
e. plotting magnitude(s) of at least one determined on-diagonal (Tpp/Tss) and/or off-diagonal ratio(s) selected from the group consisting of:
(Tps/Tpp) and (Tsp/Tss) and (Tps/Tss) and (Tsp/Tpp);
with respect to at least one parameter selected from the group consisting of:
wavelength;
xe2x80x9cPxe2x80x9d plane angle-of-incidence of an investigating polarized beam of electromagnetic radiation to an alignment surface of said material system; and
optical axis radial direction rotation angle;
and accepting said material system based upon observing said plot(s) only if said plot(s) essentially match known xe2x80x9ctemplatexe2x80x9d plots.
Another Patent, U.S. Pat. No. 5,757,494 to Green et al., is identified as it describes a method for enabling investigation of a sample system with ellipsometer systems, even in ellipsometric PSI and/or DELTA regions wherein said ellipsometer system is, without the invention, xe2x80x9cblindxe2x80x9d, (eg. DELTA of (0.0) or (180) degrees) in Rotating Polarizer and Rotating Analyzer Ellipsometer Systems, and/or (PSI or (45) degrees in Modulation Element Ellipsometer Systems). Said 494 Patent describes a method of determination of sample system PSI and DELTA values with improved accuracy and precision comprising utilizing a variable compensator, said method comprising in a functional order, the steps of:
a. providing an ellipsometer system selected from the group consisting of:
modulation element, rotatable element and rotating element;
which ellipsometer system enables accurate and precise determination of PSI and DELTA values of essentially any investigatable sample system; said ellipsometer system comprising means for setting at least one polarization state in a beam of polarized light and means for identifying, and means for monitoring a polarization state in said polarized beam of light, after an interaction thereof with a sample system;
between said means for setting at least one polarization state in a beam of polarized light and said means for monitoring a polarization state in said polarized beam of light, there being present at least one adjustable means for controlling an ellipsometric phase angle between orthogonal components in a polarized beam of light, which adjustable means for controlling an ellipsometric phase angle, in use, allows sequentially setting a plurality of ellipsometric phase angles between orthogonal components in a polarized beam of light which is caused by said ellipsometer system to interact with a sample system, such that in use said ellipsometric phase angle can be set sequentially through a plurality of settings while ellipsometric data is obtained by said means for monitoring a polarization state in said polarized beam of light at at least two selected settings of said at least one adjustable means for controlling an ellipsometric phase angle; which obtained ellipsometric data can be utilized in determination of PSI and DELTA values of an investigated sample system, where said determination of said PSI and DELTA values includes compensating for the effects on said obtained ellipsometric data of said at least two selected setting of said at least one adjustable means for controlling an ellipsometric phase angle, on said obtained ellipsometric data;
said ellipsometer system being further comprised of computational means which performs determination of investigated sample system PSI and DELTA values, which computational means utilizes data obtained with said at least one adjustable means for controlling ellipsometric phase angle between orthogonal components in a polarized beam of light, being set to at least two selected settings, and which computational means performs compensation of the effects of said at least one adjustable means for controlling ellipsometric phase angle between orthogonal components, on said utilized ellipsometric data obtained at said at least two selected settings of said at least one adjustable means for controlling ellipsometric phase angle between orthogonal components in determining sample system PSI and DELTA values;
b. placing a sample system to be investigated into said ellipsometer system and causing a beam of polarized light from said means for setting at least one polarization state in a beam of polarized light to interact therewith and enter said means for monitoring a polarization state;
c. adjusting said at least one adjustable means for controlling ellipsometric phase angle between said orthogonal components to be sequentially set to a plurality of settings while ellipsometric data is obtained by said means for monitoring a polarization state in said polarized beam of light at at least two selected settings from said plurality settings of said at least one adjustable means for controlling a value of ellipsometric phase angle between said orthogonal components;
d. causing said computational means to determine investigated sample system PSI and DELTA values by a method which performs compensation of the effects of said at least one adjustable means for controlling ellipsometric phase angle between orthogonal components in a polarized beam of light on said ellipsometric data obtained at said at least two selected settings of said at least one adjustable means for controlling ellipsometric phase angle between orthogonal components in a polarized beam of light which is caused to interact with a sample system, in determining sample system PSI and DELTA values; and
e. optionally determining at least some of members of the group consisting of:
the xe2x80x9cHandednessxe2x80x9d;
Stokes Vector; and
Jones and Mueller Matrix components;
of said polarized beam of light and investigated sample system.
(It is noted that the computational means can be any computer system with sufficient memory and processing capability).
Said method can include obtaining data comprising a plurality of relative magnitude ratios of orthogonal components and phase angles between orthogonal components are obtained, at least some of which plurality of ellipsometric relative magnitude ratios of orthogonal components and measured ellipsometric phase angles between orthogonal components correspond to sequential adjusted settings of ellipsometric relative magnitude ratios of orthogonal components present in said beam of polarized light, said sequential adjusted settings being effected by adjustment of at least one member of the group consisting of:
said means for setting at least one polarization state in a beam of polarized light; and
said means for identifying a polarization state in said polarized beam of light;
and in which said computational means is also caused to perform compensation of the effects of said sequential adjusted settings of ellipsometric relative magnitude ratios of orthogonal components present in said beam of polarized light which is caused by said ellipsometer system to interact with a sample system, in determining investigated sample system PSI and DELTA values. Said method can also involve obtaining a plurality of ellipsometric phase angles between orthogonal components which are effected at each sequential adjusted setting of ellipsometric relative magnitude ratio of orthogonal components present in said beam of polarized light which is caused by said ellipsometer system to interact with a sample system. Said 494 is disclosed as the at least one adjustable means for controlling ellipsometric phase angle between said orthogonal components to be sequentially set to a plurality of settings while ellipsometric data is obtained is a compensator which is typically utilized in practice of the present invention to determine xe2x80x9cHandednessxe2x80x9d, that is, if a value for (xcex94nxy) which is determined by present invention methodology is positive or negative.
A recent Patent to Johs et al., U.S. Pat. No. 5,872,630, is also disclosed as it describes rotating compensator ellipsometer system and a method of evaluating sample system characteristics, involving application of mathematical regression onto data acquired by application of electromagnetic beams thereto. Said 630 Patent Claims a spectroscopic rotating compensator material system investigation system comprising a source of a polychromatic beam of electromagnetic radiation, a polarizer, a stage for supporting a material system, an analyzer, a dispersive optics and at least one detector system which contains a multiplicity of detector elements, said spectroscopic rotating compensator material system investigation system further comprising at least one compensator(s) positioned at a location selected from the group consisting of:
before said stage for supporting a material system; and
after said stage for supporting a material system; and
both before and after said stage for supporting a material system;
such that when said spectroscopic rotating compensator material system investigation system is used to investigate a material system present on said stage for supporting a material system, said analyzer and polarizer are maintained essentially fixed in position and at least one of said at least one compensator(s) is caused to continuously rotate while a polychromatic beam of electromagnetic radiation produced by said source of a polychromatic beam of electromagnetic radiation is caused to pass through said polarizer and said compensator(s), said polychromatic beam of electromagnetic radiation being also caused to interact with said material system, pass through said analyzer and interact with said dispersive optics such that a multiplicity of essentially single wavelengths are caused to simultaneously enter a corresponding multiplicity of detector elements in said at least one detector system. Also Claimed is a regression based method of calibrating a spectroscopic rotating compensator material system investigation system comprising the steps of:
a. providing a spectroscopic rotating compensator material system investigation system as described;
b. developing a mathematical model of said spectroscopic rotating compensator material system investigation system which comprises as calibration parameter variables polarizer azimuthal angle orientation, present material system PSI, present material system DELTA, compensator azimuthal angle orientation(s), matrix components of said compensator(s), and analyzer azimuthal angle orientation, which mathematical model is effectively a transfer function which enables calculation of electromagnetic beam intensity as a function of wavelength detected by a detector element, given intensity as a function of wavelength provided by said source of a polychromatic beam of electromagnetic radiation;
c. causing a polychromatic beam of electromagnetic radiation produced by said source of a polychromatic beam of electromagnetic radiation, to pass through said polarizer, interact with a material system caused to be in the path thereof, pass through said analyzer, and interact with said dispersive optics such that a multiplicity of essentially single wavelengths are caused to simultaneously enter a corresponding multiplicity of detector elements in said at least one detector system, with said polychromatic beam of electromagnetic radiation also being caused to pass through said compensator(s) positioned at a location selected from the group consisting of:
before said stage for supporting a material system;
after said stage for supporting a material system; and
both before and after said stage for supporting a material system;
d. obtaining an at least two dimensional data set of intensity values vs. wavelength and a parameter selected from the group consisting of:
angle-of-incidence of said polychromatic beam of electromagnetic radiation with respect to a present material system; and
azimuthal angle rotation of one element selected from the group consisting of:
said polarizer; and
said analyzer;
over time, while at least one of said at least one compensator(s) is caused to continuously rotate;
e. performing a mathematical regression of said mathematical model onto said at least two dimensional data set, thereby evaluating calibration parameters in said mathematical model;
said regression based calibration procedure evaluated calibration parameters serving to compensate said mathematical model for non-achromatic characteristics and non-idealities of said compensator(s), and for azimuthal angles of said polarizer. Said 630 Patent is disclosed for general insight to ellipsometric procedure.
Other Patents to Johs et al. are U.S. Pat. Nos. 5,666,201 and 5,805,285. Said Patents, it is noted, describe, respectively, a spectroscopic ellipsometer and a spectroscopic spectrophotometer system, wherein a spectroscopic beam of electromagnetic radiation is caused to interact with a dispersive optics to the end that multiple orders of wavelengths are produced and detected.
Scientific articles which are of direct interest, and which are included herewithin by reference are:
xe2x80x9cOptical Characterization Of Anisotropic Plasticsxe2x80x9d, Hilfiker, Herzinger, Bungay, Woollam and Elman, Optical Interference Coatings, Op. Soc. Am, Tech. Dig. Series, Vol. 9, ((1998).
xe2x80x9cCharacterization of Bi-Axially-Stretched Plastic Films By Generalized Ellipsometryxe2x80x9d, Elman, Greener, Herzinger and Johs, Thin Solid Films, 313-314 (1998).
xe2x80x9cPhase And Microstructure Investigations Of Boron Nitride Thin Films By Spectroscopic Ellipsometry In The Visible And Infrared Spectral Rangexe2x80x9d, Franke, Schubert, Neumann, Tiwald, Thompson, Woollam, Hahn and Richter, J. Appl. Phys. 82(6), (September 1997).
xe2x80x9cDetermination Of Optical Anisotropy In Calcite From Ultraviolet To Mid-Infrared By Generalized Ellipsometryxe2x80x9d, Thompson, DeVries, Tiwald, and Woollam, Thin Solid Films, 313-314 (1998).
Additionally, an article by Johs, titled xe2x80x9cRegression Calibration Method For Rotating Element Ellipsometersxe2x80x9d, which appeared in Thin Film Solids, Vol. 234 in 1993 is also identified as it predates the Chen et al. 350 Patent and describes an essentially similar approach to ellipsometer calibration. An article by Jellison Jr. titled xe2x80x9cData Analysis for Spectroscopic Ellipsometryxe2x80x9d, Thin Film Solids, 234, (1993) is identified as it describes a method for determining the accuracy with which certain data points can be measured, which information allows adding a weighting factor to a curve fitting regression procedure as applied to a multiplicity of data points, said weighting factor serving to emphasize the effect of more accurate and precise data. A book by Azzam and Bashara titled xe2x80x9cEllipsometry and Polarized lightxe2x80x9d North-Holland, 1977 is disclosed and incorporated herein by reference for general theory. An article by Collins titled xe2x80x9cAutomated Rotating Element Ellipsometers: Calibration, Operation, and Real-Time Applicationsxe2x80x9d, Rev. Sci. Instrum. 61(8), August 1990 is identified as it provides insight into rotating element ellipsometers. An article by Kleim et al. titled xe2x80x9cSystematic Errors in Rotating-Compensator Ellipsometryxe2x80x9d published in J. Opt. Soc. Am./Vol. 11, No. 9, September 1994 is identified as it describes calibration of rotating compensator ellipsometers. An Article by An and Collins titled xe2x80x9cWaveform Analysis With Optical Multichannel Detectors: Applications for Rapid-Scan Spectroscopic Ellipsometerxe2x80x9d, Rev. Sci. Instrum., 62 (8), August 1991 is also identified as it discusses effects such as Detection System Error Characterization, Stray Light, Image Persistence etc., and calibration thereof. Also disclosed are articles by Schubert et al. which describe xe2x80x9cGeneralized Ellipsometryxe2x80x9d. The first thereof is titled xe2x80x9cExtension Of Rotating-Analyzer Ellipsometry To Generalized Ellipsometry: Determination Of The Dielectric Function Tensor From Uniaxial TiO2xe2x80x9d, J. Opt. Soc. Am. A. 13, (1996). The second such article is authored by M. Schubert alone and is titled xe2x80x9cPolarization Dependent Parameters Of Arbitrary Anisotropic Homogeneous Epitaxial Systemsxe2x80x9d, Phys. Rev. B 53, (1996). The third such article is titled xe2x80x9cGeneralized Transmission Ellipsometry For Twisted Biaxial Dielectric Media: Application To Chiral Liquid Crystalsxe2x80x9d, J. Opt. Soc. Am. A/Vol. 13, No. 9 (1996). The Schubert et al. articles, it is noted, describe ellipsometer systems which have rotatable sample system supporting stages, and primarily focus on investigation of sample systems, utilizing said ellipsometer systems, which sample systems have isotropic xe2x80x9cin-planexe2x80x9d refractive indices, (ie. where nx=ny). Further identified for authority regarding mathematical regression is a book titled Numerical Recipes in xe2x80x9cCxe2x80x9d, 1988, Cambridge University Press.
In view of the foregoing, a need remains for methodology for evaluating anisotropic refractive indices, and orientations thereof, in three dimensions.
The present invention is an ellipsometer/polarimeter, and/or spectrophotometer based method of determining values for anisotropic refractive indices (nx), (ny) and (nz) in, respectively, xe2x80x9cxxe2x80x9d, xe2x80x9cyxe2x80x9d and xe2x80x9czxe2x80x9d directions in a sample system, which xe2x80x9cxxe2x80x9d, xe2x80x9cyxe2x80x9d and xe2x80x9czxe2x80x9d directions have a determinable relationship to the orientation of an alignment surface of said sample system. The present invention method, in its preferred embodiment, because of its sequence of steps and utilization of parameter values and/or data acquired in earlier steps in later steps, requires acquisition of relatively simple and easy to acquire data sets of only one (1) dimension where refractive indices (nx), (ny) and (nz) or differences therebetween (xcex94nxy); and (xcex94nxzor (xcex94nyz) are evaluated. However, variations of said preferred method allow for use of multiple dimension data sets in mathematical regression based determination of deviation from perpendicular to a sample system alignment surface regarding the direction of an out-of-plane (nz) refractive index, or where, for instance, separately identifiable steps are combined, or where it is desired to determine dispersion characteristics of one or more refractive indices which have previously been evaluated at a single wavelength. The essence of the preferred present invention method can be recited as sequentially involving at least four basic steps, said four basic steps being:
Determining the precise orientation of a third orthogonal index (nz) of refraction which projects essentially perpendicular to an alignment surface of a sample system, said alignment surface being characterized by two essentially in-plane orthogonal, (ie. (nx) and (ny)), indices of refraction;
Causing a spectroscopic beam of electromagnetic radiation originating from a source of a beam of electromagnetic radiation, (which spectroscopic beam of electromagnetic radiation is preferably essentially linearly polarized and is comprised of a plurality of wavelengths for which said sample system is essentially transparent), to approach said alignment surface of said sample system along a locus which is essentially co-incident with the orientation of the third orthogonal index (nz) of refraction, at least partially transmit through said sample system and enter a transmission detector to the end that a one-dimensional data set as a function of wavelength is acquired; and applying a computational means which is programmed with a mathematical model for said sample system to the end that a value for the difference between the in-plane (xcex94xy) indices of refraction and the Euler angle orientations of said essentially in-plane orthogonal (nx) (ny) indices of refraction are determined;
Causing a beam of electromagnetic radiation originating from said source of a beam of electromagnetic radiation, (which beam of electromagnetic radiation is preferably essentially linearly polarized and is comprised of at least one wavelength), to approach said alignment surface of said sample system along a plurality of near normal angles-of-incidence to said sample system alignment surface, interact with said sample system and enter said transmission and/or reflection detector to the end that a one dimensional data set as a function of angle-of-incidence is acquired; and applying said computational means which is programmed with a mathematical model for said sample system to the end that a value for the difference between at least one out-of-plane combination of indices of refraction selected from the group consisting of (xcex94xz), and (xcex94nyz) is determined; and
Causing a beam of electromagnetic radiation originating from said source of a beam of electromagnetic radiation, (which beam of electromagnetic radiation is preferably essentially linearly polarized and is comprised of at least one wavelength), to approach said alignment surface of said sample system along a plurality of angles-of-incidence at near the Brewster condition to said sample system alignment surface, interact with said sample system and enter said reflection and/or transmission detector to the end that data as a function of angle-of-incidence is acquired; and applying said computational means which is programmed with a mathematical model for said sample system to the end that an absolute value for at least one index of refraction selected from the group consisting of (nx), (ny) and (nz) is/are directly determined, and, if desired or required, from previously determined values for (xcex94nxy), (xcex94nxz) and (xcex94nyz), determining absolute values for (nx), (ny) or (nz) not directly evaluated.
It is believed that the present invention Patentability is found in two areas:
1. specific method step sequences, which sequences, in later steps thereof, utilize results secured in earlier steps thereof, in mathematical, (eg. square error reducing regression), procedures which operate on said data acquired in said later steps; and
2. only one dimensional data sets need be generated in steps of the preferred embodiment, where values for refractive indices (nx), (ny) and (nz) or differences therebetween (xcex94nxy); and (xcex94nxz) or (xcex94nyz) are evaluated.
Continuing, while the present invention can be practiced utilizing various optical systems, including polarimeters or spectrophotometers, ellipsometers are disclosed as the preferred systems. In that light, for demonstrative insight, the following brief description of ellipsometric procedure is presented. The practice of ellipsometry requires providing an ellipsometer system, (see FIG. 1), comprised elements selected from a group including:
1. a source of a beam of electromagnetic radiation (LS);
2. a polarizer (P);
3. a stage for supporting a sample system (STG);
4. an analyzer (A);
5. a reflection detector (DET-REFLECTION);
6. a transmission detector (DET-TRANSMISSION);
7. a compensator ((C), (Cxe2x80x2) (Cxe2x80x3) at some point between said polarizer (P) and analyzer (A); and
8. a modulation element at some point between said polarizer (P) and analyzer (A);
and it is to be understood that typically associated with an ellipsometer system is a computational means which is programmed with a mathematical model of the ellipsometer system and of a sample system being investigated. The mathematical model of the ellipsometer system typically comprises matrices, or mathematical equivalents, for the source of the beam of electromagnetic radiation, for the polarizer and for the analyzer and detector, and comprises a mathematical model for the sample system, including thicknesses and refractive indices of various surface layers, and parameters which identify anisotropic refractive indices (nx), (ny), (nz), and directions xe2x80x9cxxe2x80x9d, xe2x80x9cyxe2x80x9d and xe2x80x9czxe2x80x9d thereof, and differences between (nx) and (ny), (xcex94nxy) and differences between (nx) and (nz), (xcex94nxz) and differences between (ny) and (nz), (xcex94nyz). Said mathematical model can also include Jones Matrix elements. Said computational means also includes a square error reducing routine for fitting numbers to said mathematical model parameters in view of experimental data obtained when a beam of single wavelength, or polychromatic, electromagnetic radiation is caused to interact with a sample system, (which is oriented in some desired state of rotation about an axis perpendicular to the alignment surface thereof), at one or various angles of incidence. Also, while it is typical that a beam of electromagnetic radiation which is caused to transmit through or reflect from a sample system surface will have orthogonal components therein retarded by differing amounts, it is further typical that said retardation difference is usually not so large that the intensity of the emerging transmitted or reflected electromagnetic beam can not be found by assuming mathematical coherent addition of said orthogonal components. However, particularly where a sample system demonstrates a large degree of anisotropy, it can occur that orthogonal components of an electromagnetic beam caused to interact therewith will be subjected to greatly differing amounts of retardation by interaction therewith. Where this occurs, it is necessary to assume orthogonal beam electric field components add incoherently to arrive at a valid intensity. In some cases assuming partial coherent:
I=(E1+E2+ . . . EN)*(E1+E2+ . . . EN)*
and partial incoherent:
I=(E1*E1*)+(E2*E2)+ . . . (EN*EN*)
addition of orthogonal electric field components can be appropriate, (eg. where pertinent data is obtained with the ellipsometer system set in a reflection mode configuration, and where a reflection detector is utilized and a transparent sample system does not have a backside thereof roughened). It is noted that the J. A. Woollam Co. Inc. W-VASE (Registered Trademark), program includes Backside Reflection Compensation capability. Note, the partitioning of a beam of electromagnetic radiation into portions which present separately with electric field components which add coherently, and incoherently, as a result of interaction with a patterned substrate, is described in a recently Allowed U.S. Pat. No. 5,936,734 to Johs and Herzinger.
It is further beneficial to emphasize that data sets can be produced by ellipsometer, polarimeter and spectrophotometer systems, which are single or multiple dimensional. That is, for instance, data as a function of:
a. wavelength; and/or
b. angle-of-incidence of a beam of electromagnetic radiation with respect to a normal to a sample system alignment surface; and/or
c. rotation of said sample system about said normal to a sample system alignment surface;
can be obtained. Further, most prior art methodology identifies the number of parameters in a mathematical model of a sample system which require evaluation, and based thereupon determine the dimensionality of data set which is required. Simultaneous mathematical regression of the mathematical model onto the sufficient data set is typically utilized to arrive at values, and confidence intervals thereof, for all mathematical model parameters. It is also noted that the reason a data set must be of xe2x80x9csufficientxe2x80x9d dimensionality, is that the procedure of mathematical regression evaluation of values for parameters in a mathematical model can fail because of xe2x80x9ccorrelationxe2x80x9d between parameters, and only a sufficiently xe2x80x9cstrongxe2x80x9d data set can avoid this pit-fall. Correlation, it is noted, refers to the situation wherein, for instance, two parameters are interrelated, such as components of a product term, which product term is directly evaluated by a mathematical regression onto a data set, (eg. refractive index (n) multiplied by a sample system thickness (t)), which product term can be arrived at by many combinations of the (n) and (t) components thereof. Use of a sufficiently strong data set, (eg. data sets obtained from two sample systems of similar refractive index (n) but different thicknesses (t1) and (t2)), in a mathematical regression procedure, can however, allow independent evaluation of the components, (ie. (n) and (t1) and (t2), of the product. In that light, it is again pointed out that the preferred embodiment of the present invention methodology provides a sequence of steps which enables use of a single dimensioned data set at each step where anisotropic refractive indices or differences therebetween are evaluated, while avoiding correlation of evaluated mathematical model parameters. This is achieved by limiting the number of parameters to be evaluated at each step where mathematical regression is applied.
Continuing, a present invention method of determining values for anisotropic refractive indices (nx), (ny) and (nz) in, respectively, xe2x80x9cxxe2x80x9d, xe2x80x9cyxe2x80x9d and xe2x80x9czxe2x80x9d directions in a sample system begins with the providing of an ellipsometer or polarimeter or spectrophotometer system comprised of selections from the group consisting of:
1. a source of a beam of electromagnetic radiation;
2. a polarizer;
3. a stage for supporting a sample system;
4. an analyzer;
5. a reflection detector;
6. a transmission detector;
7. a compensator at some point between said polarizer and analyzer;
8. a modulation element at some point between said polarizer and analyzer; and
9. a computational means which is programmed with a mathematical model for said sample system, said mathematical model serving to relate indices of refraction, thickness and optical axis direction over a range of at least one member of the group consisting of:
wavelength;
xe2x80x9cPxe2x80x9d plane angles-of-incidence of an investigating polarized beam of electromagnetic radiation to an alignment surface of said material system; and
optical axis radial direction rotation angle;
which computational means includes a mathematical, (eg. square error reducing), routine for fitting numbers to said mathematical model parameters in view of experimental data, and which can include analysis capabilities based upon accounting for coherent and incoherent addition of electromagnetic components in calculation of intensity, as occurs where backside reflections are present. (Note, the Patent to Johs, U.S. Pat. No. 5,872,630, discussed in the Background Section of this Disclosure describes use of such a computational means for use in mathematical modeling in the case of a Rotating Compensator Ellipsometer System, and wherein mathematical regression is performed onto a two-dimensional data set).
(It is noted that the terminology xe2x80x9ccomputational meansxe2x80x9d includes any computer system with sufficient input, memory, processing capability and output means).
As alluded to above, said method further involves providing a sample system having two essentially in-plane (nx) (ny) orthogonal indices of refraction in an alignment surface thereof and a third (nz) index of refraction which projects essentially perpendicular to said alignment surface of said sample system, then determining the thickness of said sample system as well as a range of wavelengths for which said sample system is essentially transparent. (It should be appreciated that the two in-plane (nx) (ny) orthogonal indices of refraction typically are of different values). Said thickness determination is often accomplished by non-ellipsometric techniques, (eg. by use of calipers), although it is again noted that if at least two sample systems which are similar in composition, but of different thickness dimensions are simultaneously investigated, the J. A. Woollam Co. W-VASE (Registered Trademark) program allows simultaneous regression onto data obtained from investigation of both said sample systems, and that generally allows breaking correlation between thickness and refractive indices with the result that a sample system thickness can be obtained by the ellipsometric techniques.
Continuing, said method further involves placing said sample system on the stage for supporting a sample system so that said alignment surface of said sample system is accessible by a beam of electromagnetic radiation originating from said source of a beam of electromagnetic radiation.
Said method also involves determining the precise orientation of the third (nz) index of refraction which projects essentially perpendicular to said alignment surface thereof, by a technique such as described in U.S. Pat. No. 5,835,222 to Herzinger, and briefly disclosed in the Background Section of this Disclosure. This step, it is noted, can optionally involve the acquisition of a two dimensional data set, as deviation of an (nz) direction from a precise normal to an alignment surface of a sample system, as well as the direction of a xe2x80x9cPxe2x80x9d-plane projection thereof in the alignment surface of the sample system can be unknown. However, qualitative observation of plotted one dimensional data sets prior to proceeding with any data set acquisition for use in quantitative regression procedures, can provide insight to good approximate starting values for the unknown related to the (nz) direction deviation from a precise normal to an alignment surface of a sample system, as well as the direction of a xe2x80x9cPxe2x80x9d-plane projection thereof in the alignment surface of the sample system. For instance, obtaining data utilizing a beam of electromagnetic radiation directed normal to an alignment surface of a sample system as a function of sample system rotation about said normal to said alignment surface can, in some cases, provide a sufficient data set for use in a regression procedure that allows precise characterization of the direction of (nz) direction deviation from a precise normal to an alignment surface of a sample system, as well as the direction of a xe2x80x9cPxe2x80x9d-plane projection thereof in the alignment surface of the sample system. Such a non-limiting procedure, which sequentially requires obtaining only one dimensional data sets, comprises:
a. by ellipsometric techniques effectively obtaining a plot of a sample system PSI ("psgr") vs. sample system rotation angle about a perpendicular to a surface of said sample system, and therefrom determining the in-plane angle at which the plane of incidence of said ellipsometric beam of electromagnetic radiation includes the direction of (nx) or (ny), by noting where minima and/or maxima occur in said effective plot; and
b. with the plane of incidence of said ellipsometric beam of electromagnetic radiation positioned as determined in step a., so as to include the direction of (nx) or (ny), effectively obtaining a plot of a DELTA (xcex94) vs. ellipsometric electromagnetic beam angle-of-incidence about a normal to the surface of said sample system, and therefrom determining a minima and/or maxima symetry point in said effective plot, said minima and/or maxima symetry point being identifying of the projected direction of (nz) in said ellipsometric electromagnetic beam plane of incidence;
such that sample system rotation angle PHI (xcfx86), about a perpendicular to the surface of said sample system, at which the ellipsometric beam of radiation plane of incidence includes the direction of (nz), and the angle of said projected direction of (nz) with respect to the normal to the sample system surface, are determined.
It is again emphasized at this point that the preferred method of the present invention requires that only one (1) dimensional data sets need be obtained when practicing any of the steps of the present invention method, and it is the case that only one (1) dimensional data sets need be obtained in the steps which directly follow wherein anisotropic refractive indices or differences therebetween are evaluated.
In the following, it should be kept in mind that the present invention method steps which result in evaluating (xcex94nxy); and (xcex94nxz) or (xcex94nyz), can be practiced in either order. That is, the steps leading to evaluation of (xcex94nxy) can be determined first, or the steps leading to evaluation of (xcex94nxz) or (xcex94nyz) can be practiced first. However, practically, it is preferred to practice the steps which allow determining (xcex94nxy) first as if the order of steps is reversed such that (xcex94nxz) or (xcex94nyz) is determined first, then it might be required to practice the steps which provide (xcex94nxy) and those which provide (xcex94nxz) or (xcex94nyz) itteratively more than once.
The preferred present invention method further then involves causing a spectroscopic beam of electromagnetic radiation originating from said source of a beam of electromagnetic radiation, (which spectroscopic beam of electromagnetic radiation is comprised of a plurality of wavelengths for which said sample system is transparent), to preferably become essentially linearly polarized and approach the alignment surface of a sample system along a locus which is essentially co-incident with the previously determined precise orientation of the third index of refraction (nz). (This eliminates the effect of said third index of refraction (nz) on orthogonal components of the beam of electromagnetic radiation and decreases sensitivity to absolute values of (nx) and (ny). A transmitted portion of said beam of electromagnetic radiation is caused to exit said sample system enter said transmission detector which mediates the collection of data therefore. (Note that where physical limitations do not prevent placement of a reflection detector, reflection data can also, or instead of, transmission data, be acquired and utilized). Said collected spectroscopic data, along with known sample system thickness and the projection direction of (nz), is then analyzed by applying said computational means which is programmed with a mathematical model for said sample system, to the end that a value for the difference between the in-plane (xcex94nxy) indices of refraction and the Euler angle PHI (xcfx86) orientations (see FIG. 2), of said in-plane orthogonal (nx) and (ny) indices of refraction are determined. This is typically achieved via application of a mathematical regression. Again, it is to be understood that aligning the beam of electromagnetic radiation along the direction of the third index of refraction (nz) focuses the procedure on determination of the difference between the in-plane (xcex94nxy) indices of refraction, and prevents said (nz), and absolute values of (nx) and (ny) indices of refraction, from having any effect in this step. It is also to be appreciated that there is always ninety (90) degrees between said in-plane orthogonal (nx) and (ny) indices of refraction, and that obtaining Jones Matrix Element Intensities:
Tpp, Tss, Tsp and/or Tps
or Intensities of Ratios of Jones Matrix Elements:
(Tpp/Tss);
(Tsp/Tss);
(Tps/Tss);
(Tsp/Tpp);
and/or
(Tps/Tpp);
as a function of a one dimensional data set, (ie. as a function of wavelength), provides sufficiently strong data to allow evaluation of the difference between the in-plane (xcex94nxy) indices of refraction and the Euler angle PHI (xcfx86) orientations of said in-plane orthogonal (nx) (ny) indices of refraction, relative to the measurement geometry xe2x80x9cPxe2x80x9d and xe2x80x9cSxe2x80x9d planes. In fact, where good approximation values for the previously determined direction of the third index of refraction (nz) are known, it is possible to let it xe2x80x9cfloatxe2x80x9d as well during a regression procedure onto said one dimensional data set as a function of wavelength, and arrive at somewhat improved values therefore, as well as for (xcex94nxy) and Euler angle orientations, in this step.
Continuing, a beam of electromagnetic radiation originating from said source of a beam of electromagnetic radiation, (which beam of electromagnetic radiation is comprised of at least one wavelength for which said sample system is essentially transparent), is preferably caused to become essentially linearly polarized and approach said alignment surface of said sample system along a plurality of angles-of-incidence, (eg. in a range including perhaps at least about negative twenty (xe2x88x9220) to positive twenty (+20) degrees and typically over a range of negative forty-five (xe2x88x9245) to positive forty-five (+45) degrees with respect to the direction of the (nz) index of refraction, which is essentially normal to the alignment surface of a sample system), to said sample system surface, partially transmit through said sample system and partially reflect therefrom and enter said transmission and/or reflection detector, which mediates the collection of data therefore, as a function of angle-of-incidence. Thereafter, said computational means which is programmed with a mathematical model for said sample system is applied to said just acquired data along with already known system thickness and the value for the difference between the in-plane (xcex94nxy) indices of refraction and the Euler angle orientations of said in-plane orthogonal (nx) (ny) indices of refraction and the orientation of the out-of-plane (nz) to the end that a value for the difference between at least one out-of-plane combination of indices of refraction selected from the group consisting of:
(xcex94nxz);
and
(xcex94nyz);
and is determined. It should now also be appreciated that if (xcex94nxy), and one of (xcex94nxz) and (xcex94nyz) is determined, then the third thereof is indirectly determined as well.
It is generally noted that where an electromagnetic beam of radiation impinges upon a sample system surface at a near-to-normal angle-of-incidence and even at upwards of 25 degrees thereto, where transmission data is obtained, the effects of absolute refractive index, (ie. nx, ny and nz), values are negligible. For this, and other reasons, values of (xcex94nxy), (xcex94nxz) and (xcex94nyz) can be determined as just described, whereas absolute refractive index difference values are typically completely obscured during said determination. It is noted that, for instance, reflection ellipsometry practiced with an electromagnetic beam directed at a sample system surface at a near Brewster Angle angle-of-incidence, (which for semiconductors is approximately seventy-five (75) degrees), allows determination of absolute refractive index values, where sample system backside reflections are accounted for. (Backside reflections can be prevented by, for instance, xe2x80x9croughening-upxe2x80x9d the backside of the investigated sample substrate). Generally then, near normal angles-of-incidence maximize sensitivity to differences in refractive indices, and oblique, near Brewster angle angles-of-incidence maximize sensitivity to absolute refractive indices effects. The present invention methodology advantageously utilizes this xe2x80x9cseparated-outxe2x80x9d determination of (xcex94xy), (xcex94nxz) and/or (xcex94nyz) by use of xe2x80x9cnear normalxe2x80x9d angles of incidence during data acquisition utilizing transmission mode ellipsometry.
Continuing, the present invention method next involves causing a beam of electromagnetic radiation which originates from said source of a beam of electromagnetic radiation, which beam of electromagnetic radiation is comprised of at least one wavelength, to preferably become essentially linearly polarized and approach said surface of said sample system along a plurality of angles-of-incidence at near the Brewster condition to said sample system surface, partially reflect from said alignment surface of said sample system and enter said reflection detector which mediates the collection of data therefore as a function of angle-of-incidence. Thereafter, said computational means which is programmed with a mathematical model for said sample system, is applied to said acquired data along with already known system thickness and the value for the difference between the in-plane (xcex94nxy) indices of refraction and the Euler angle orientations of said in-plane orthogonal (nx) (ny) indices of refraction are determined, and the known difference between at least one out-of-plane combination of indices of refraction selected from the group consisting of:
(xcex94nxz);
and
(xcex94nyz);
to the end that an absolute value for at least one index of refraction selected from the group consisting of:
(nx);
(ny);
(nz);
is/are determined. Then, as required, utilizing previously determined values for (xcex94nxy), (xcex94nxz) and (xcex94nyz), absolute values for all (nx), (ny) and (nz) are determined.
It is noted that determination of at least one index of refraction selected from the group consisting of:
(nx);
(ny);
(nz);
can include accounting for sample system back-side reflections by, for instance, application of incoherent electric field component addition. The J. A. Woollam CO. W-VASE (Registered Trademark) software provides this capability.
It is further noted that determination of a value for the difference between the in-plane (xcex94nxy) indices of refraction and the Euler angle orientations of said in-plane orthogonal (nx) (ny) indices of refraction typically involves obtaining and utilizing data acquired with said compensator in two positions, (eg. present and not-present), in order to specifically identify a non-ambiguous, xe2x80x9chandednessxe2x80x9d determined value for (xcex94nxy).
It is emphasized that the foregoing specifies definite acquisition of transmission, or of reflection, data in the various steps. However, after the determination of the direction of the deviation of an (nz) direction from a precise normal to an alignment surface of a sample system, as well as the direction of any in-plane projection thereof in the alignment surface of the sample system, it is generally the case that either transmission or reflection data can be utilized, where physical space limitations regarding placement of detectors etc. allow. This is because an electromagnetic beam, (of a wavelength at which a sample system is substantially transparent), which is caused to interact with a sample system by impinging on its alignment surface, partially transmits and partially reflects from said alignment surface of said sample system, with the portions of the beam which transmit and reflect being largely dependent on the angle of incidence of said electromagnetic beam to the alignment surface. As both the transmitted and reflected beams contain similar information, either transmission or reflection beams can then, where physically possible, be detected and utilized in essentially all steps and be within the scope of the present invention. Also, it must be appreciated that data acquired can be anisotropic intensity data or anisotropic ellipsometric data. However, in a practical sense, as the identification of the orientation of the (nz) index of refraction can require evaluation of very small deviation angles from a perpendicular to an alignment surface of a sample system, it is usually necessary to utilize ellipsometric data obtained from a transmission detector to allow determination of said deviation angles, as transmission through a large thickness of an anisotropic sample substrate provides measurable data which typically does not appear in reflection data, especially when reflection data is complicated by back-side reflections and physical restraints of detector location placement.
It is again noted that qualitative steps can provide insight to the approximate orientation of (nz) and further augment the recited present invention quantitative method. For instance, prior to any quantitative data acquisition, data obtained by use of electromagnetic beam investigation of the sample system can be plotted and subjected to visual evaluation to determine relative anisotropy effects of xe2x80x9cin-planexe2x80x9d indices of refraction (nx) and (ny) on said beam of electromagnetic radiation which is caused to pass through a thickness (t) of a sample system. Said data can be ellipsometric or intensity, as a function of wavelength or angle-of-incidence or sample system rotation. Intensity or ellipsometric data vs. sample rotation angle is also useful in determining the orientation of in-plane nx and ny refractive indices with respect to xe2x80x9cPxe2x80x9d and xe2x80x9cSxe2x80x9d directions, as well as to determine the direction of nz with respect to a normal to an alignment surface of the sample system under investigation. Further, if there is minimal difference between the effect of the in-plane (nx*t) and (ny*t) on a beam of electromagnetic radiation there will be few xe2x80x9cwigglesxe2x80x9d on a plot of anisotropic intensity(s), (ie. Jones Matrix components tpp, tss, tps, tsp) or ellipsometric ratios thereof, as a function of wavelength, and if there is a relatively large difference between the effect of the (nx*t) and (ny*t) on a beam of electromagnetic radiation there will be many xe2x80x9cwigglesxe2x80x9d on a plot of intensity or ellipsometric data as a function of, for instance, wavelength. Where plots as a function of angle-of-incidence are observed, out-of-plane differences in refractive indices can be estimated, (ie. differences between (nz*t) and either (nx*t) or (ny*t), by observation of xe2x80x9cwigglesxe2x80x9d in intensity or ellipsometric, (ie. Jones Matrix components tpp, tss, tps, tsp or ratios thereof), data plotted as a function of said near-normal angles-of-incidence. Generally, it has been found beneficial to use the information so gleened to determine how to orient linear xe2x80x9cPxe2x80x9d-plane polarization direction of the beam of electromagnetic radiation with respect to the direction of the xe2x80x9cin-planexe2x80x9d indices of refraction, (nx) and (ny) of a sample system. If few xe2x80x9cwigglesxe2x80x9d are observed in the identified plots as functions of wavelength and/or near-normal angles-of-incidence, it is has often been found best to orient said linearly polarized beam so that its P-Plane locus bisects the directions of the xe2x80x9cin-planexe2x80x9d indices of refraction, (nx) and (ny) in following steps of the present invention method; and if many xe2x80x9cwigglesxe2x80x9d are observed, it is often best to orient said linearly polarized beam""s xe2x80x9cPxe2x80x9d-plane so that it is oriented essentially along a direction of one of the xe2x80x9cin-planexe2x80x9d indices of refraction, (nx) and (ny) in said following steps of the present invention method. Hence, the present invention method of determining values for anisotropic refractive indices (nx), (ny) and (nz) in, respectively, xe2x80x9cxxe2x80x9d, xe2x80x9cyxe2x80x9d and xe2x80x9czxe2x80x9d directions in a sample system can further comprise a preliminary qualitative step of obtaining data selected from the group consisting of:
transmission anisotropic intensity data;
transmission anisotropic ellipsometric data;
reflection anisotropic intensity data; and
reflection anisotropic ellipsometric data;
as a function of a selection from the group consisting of:
angle-of-incidence; and
wavelength;
and observing said data for the presence of xe2x80x9cwigglesxe2x80x9d. Based upon said observation one then orients said sample system as described by a selection from the group consisting of:
1. so said linearly polarized beam locus bisects the directions of the xe2x80x9cin-planexe2x80x9d indices of refraction, (nx) and (ny);
2. so said linearly polarized beam locus essentially aligns with the direction of one of the xe2x80x9cin-planexe2x80x9d indices of refraction, (nx) and (ny).
FIG. 10 is included to demonstrate how the xe2x80x9cwigglesxe2x80x9d alluded to can appear in real ellipsometric PSI ("psgr") data as a function of angle-of-incidence. The actual data shown is PSI ("psgr") for a TiO2 crystal, as a function of near-normal angle-of-incidence
It is further to be appreciated that once the values for (xcex94nxy), (xcex94nxz) and (xcex94nyz), and absolute values for all (nx), (ny) and (nz) and the directions (x), (y) and (z) thereof with respect to the alignment surface, are determined, an optional additional step is to obtain a multi-dimensional data set and re-evaluate all said values simultaneously to verify accuracy, and to provide dispersion information not acquired in steps where spectroscopic data was not utilized. Said additional step is much like what conventional ellipsometric methods utilize, but with the benefit of having very good, previously determined starting values for (xcex94nxy), (xcex94nxz) and (xcex94nyz), and for absolute values for all (nx), (ny) and (nz), and for the directions (x), (y) and (z) thereof with respect to the alignment surface, being available.
It is again generally pointed out that the present invention has determined the fact that where it is desired to determine differences in in-plane, (ie. xcex94nxy), refractive indices, then electromagnetic radiation should be directed along the direction of the out-of-plane refractive index (nz) and transmission data should be acquired and utilized in regression procedures. Where out-of-plane differences between refractive indices (ie. xcex94nxz) and (xcex94nyz)), is/are to be determined, then electromagnetic radiation of at least one wavelength should be utilized and directed along near-normal angles-of-incidence around a normal to a sample system reference surface, and either transmission or reflection data acquired and utilized in regression procedures. And, where it is desired to evaluate absolute value(s) of one or more refractive indices (ie. (nx), (ny) and (nz)), in an anisotropic sample system, then reflectance, and/or transmission data obtained utilizing angles-of-incidence at and/or around the Brewster angle are preferably utilized. Refinements in practicing the present invention include orienting an ellipsometer electromagnetic beam plane of incidence with, or between in-plane, (ie. (nx), (ny)), indices of refraction during the obtaining of data at near normal angles-of-incidence, and correcting for sample system backside reflections when obtaining reflectance data at near Brewster angles-of-incidence.
The present invention will be better understood by reference to the Detailed Description Section of this Disclosure, in conjunction with the Drawings.
An objective and/or purpose of the present invention is to provide a method of evaluating anisotropic sample system indices of refraction (nx), (ny) and (nz) and orientations thereof with respect to an alignment surface of said sample system, said method comprising a sequence of steps which require that only relatively simple one-dimensional data sets be acquired.
Another objective and/or purpose of the present invention is to provide a method of evaluating anisotropic sample system indices of refraction (nx), (ny) and (nz) and orientations thereof with respect to an alignment surface of said sample system, which method utilizes data sets acquired with electromagnetic beams oriented at near-normal incidence to an alignment surface of said sample system so that the difference between the in-plane (xcex94nxy) indices of refraction and the Euler angle orientations of said in-plane orthogonal (nx) (ny) indices of refraction are determined, and so the difference between at least one out-of-plane combination of indices of refraction selected from the group consisting of:
(xcex94nxz);
and
(xcex94nyz);
can be determined.
Yet another objective and/or purpose of the present invention is to provide a method of evaluating absolute values for anisotropic sample system indices of refraction (nx), (ny) and (nz), and orientations thereof with respect to an alignment surface of a sample system; which method utilizes data obtained at near Brewster angle angles-of-incidence, in combination with previously obtained values for (xcex94nxy) and (xcex94nxz) or (xcex94nyz), which were evaluated utilizing data sets obtained at near normal angles-of-incidence.
Another, general objective and/or purpose of the present invention is to particularly point out that ellipsometric or intensity transmission and/or reflection data obtained by investigation of a sample system utilizing angles-of-incidence which are near-normal to a surface of said sample system, are predominately sensitive to differences between orthogonal indices of refraction; while ellipsometric or intensity transmission or reflection data obtained by investigation of a sample system utilizing angles-of-incidence which are near the Brewster angle of a sample system, (where backside reflections are appropriately accounted for), are predominately sensitive to absolute values of in-plane refractive indices (nx) or (ny); and further, that spectroscopic transmission ellipsometric or intensity data obtained with an incident beam of electromagnetic radiation oriented along the direction of an out-of-plane refractive index (nz) is identified as particularly sensitive to (xcex94nxy), and transmission or reflection ellipsometric or intensity data obtained with an incident beam of electromagnetic radiation oriented at numerous near normal angles-of-incidence is identified as particularly sensitive to (xcex94nxz) or (xcex94nyz).
Other objectives and/or purposes of the present invention will become apparent by reference to the Specification.